where Q is a complex unitary distributed matrix defined as the
product of K elementary reflectors

Q = H(k) . . . H(2) H(1)

as returned by PCGEQLF. Q is of order M if SIDE = L and of order N
if SIDE = R.

Notes
=====

Each global data object is described by an associated description
vector. This vector stores the information required to establish
the mapping between an object element and its corresponding process
and memory location.

Let A be a generic term for any 2D block cyclicly distributed array.
Such a global array has an associated description vector DESCA.
In the following comments, the character _ should be read as
"of the global array".

NOTATION STORED IN EXPLANATION
--------------- -------------- --------------------------------------
DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
DTYPE_A = 1.
CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
the BLACS process grid A is distribu-
ted over. The context itself is glo-
bal, but the handle (the integer
value) may vary.
M_A (global) DESCA( M_ ) The number of rows in the global
array A.
N_A (global) DESCA( N_ ) The number of columns in the global
array A.
MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
the rows of the array.
NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
the columns of the array.
RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
row of the array A is distributed.
CSRC_A (global) DESCA( CSRC_ ) The process column over which the
first column of the array A is
distributed.
LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
array. LLD_A >= MAX(1,LOCr(M_A)).

Let K be the number of rows or columns of a distributed matrix,
and assume that its process grid has dimension p x q.
LOCr( K ) denotes the number of elements of K that a process
would receive if K were distributed over the p processes of its
process column.
Similarly, LOCc( K ) denotes the number of elements of K that a
process would receive if K were distributed over the q processes of
its process row.
The values of LOCr() and LOCc() may be determined via a call to the
ScaLAPACK tool function, NUMROC:
LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
An upper bound for these quantities may be computed by:
LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A

to an array of dimension (LLD_A,LOCc(JA+K-1)). On entry, the
j-th column must contain the vector which defines the elemen-
tary reflector H(j), JA <= j <= JA+K-1, as returned by
PCGEQLF in the K columns of its distributed matrix
argument A(IA:*,JA:JA+K-1). A(IA:*,JA:JA+K-1) is modified by
the routine but restored on exit.
If SIDE = L, LLD_A >= MAX( 1, LOCr(IA+M-1) ),
if SIDE = R, LLD_A >= MAX( 1, LOCr(IA+N-1) ).

IA (global input) INTEGER

The row index in the global array A indicating the first
row of sub( A ).

JA (global input) INTEGER

The column index in the global array A indicating the
first column of sub( A ).

DESCA (global and local input) INTEGER array of dimension DLEN_.

The array descriptor for the distributed matrix A.

TAU (local input) COMPLEX, array, dimension LOCc(JA+N-1)

This array contains the scalar factors TAU(j) of the
elementary reflectors H(j) as returned by PCGEQLF.
TAU is tied to the distributed matrix A.

C (local input/local output) COMPLEX pointer into the

local memory to an array of dimension (LLD_C,LOCc(JC+N-1)).
On entry, the local pieces of the distributed matrix sub(C).
On exit, sub( C ) is overwritten by Q*sub( C ) or Q*sub( C )
or sub( C )*Q or sub( C )*Q.

IC (global input) INTEGER

The row index in the global array C indicating the first
row of sub( C ).

JC (global input) INTEGER

The column index in the global array C indicating the
first column of sub( C ).

ILCM, INDXG2P and NUMROC are ScaLAPACK tool functions;
MYROW, MYCOL, NPROW and NPCOL can be determined by calling
the subroutine BLACS_GRIDINFO.

If LWORK = -1, then LWORK is global input and a workspace
query is assumed; the routine only calculates the minimum
and optimal size for all work arrays. Each of these
values is returned in the first entry of the corresponding
work array, and no error message is issued by PXERBLA.

INFO (global output) INTEGER

= 0: successful exit
< 0: If the i-th argument is an array and the j-entry had
an illegal value, then INFO = -(i*100+j), if the i-th
argument is a scalar and had an illegal value, then
INFO = -i.

Alignment requirements
======================

The distributed submatrices A(IA:*, JA:*) and C(IC:IC+M-1,JC:JC+N-1)
must verify some alignment properties, namely the following
expressions should be true: